After installing my oil coolers (twin tube Wimmer oil coolers) I added oil the same way I do for any oil change. I put 3 quarts in the bag and ran the engine for a couple of minutes to distribute the oil into the engine, filter, lines, oil coolers and passageways and to check for leaks. Then I shut the engine off and topped off the oil tank until it measured halfway between 'Add' and 'Full' on the dipstick. So, I have no idea how much "extra" oil I added. I added whatever was necessary.
With 3 quarts to start with there is no way it will run dry.
Not trying to state what's best but when I had an oil cooler installed the regular amount was added and then normal oil checks performed and oil added until it showed the correct level. Turns out it was about a quart more in my case.
All said n' done, I would be curious what diff in oil temps it makes.
This thing of mine runs 250 on a hot day.
Not to step on the original author but for mine I never put a thermometer on. Our climate (Ontario) doesn't see the temps many experiance South of us. I liked having the additional oil capacity and a little extra cooling.